[Dune] YaspGrid, periodicity and boundary segment indices

[Martin Nolte]

Hi Atgeirr,

the subject of periodic grids in DUNE has been raised quite a few times.
Yet, a real discussion on the subject is lacking since the 2008
developer meeting in Heiderberg. For a start, you might want to take a
look at the FlySpray tasks 367, 442, and 469. To my knowledge, it is not
clear whether YaspGrid works properly in a periodic setting (I think the
grid check still fails).

Apart from that, there are other grids supporting periodic boundaries,
e.g., AlbertaGrid and ALUGrid. I used the term periodic boundaries
intentionally, since they only support periodic boundary conditions and
do not try to model a toroidal topology. In this approach, the
intersection iterator on a periodic boundary will return an outside
entity, which is simply the element "on the other side". Otherwise, the
grid does not behave differently from a non-periodic one. The obvious
advantage is the ease of implementation. To solve a Laplace equation
with continuous finite elements on the unit square subject to periodic
boundary conditions is, at first sight, an extra load of work, because
degrees of freedom have to be identified. But this has to be done only
once (in the user code) and not for every grid. Finite volume schemes,
of course, work out of the box (apart from higher order reconstructon).

I hope this helps a little. Periodicity should, of course, be a topic on
one of the next developer meetings, but I think there are currently more
pressing issues in the interface (at least to the developers).

Best,

Martin

On 06/03/2011 09:47 AM, Atgeirr Rasmussen wrote:
> Dear Dune,
> 
> I have some problems understanding what the proper behaviour of boundary segment indices should be.
> I am currently updating our grid class CpGrid to properly support periodicity, and so I am looking at YaspGrid to get an impression of what's correct.
> (I am currently on revision 7633 of dune-grid, in case that matters)
> 
> The program listed at the bottom constructs a 3x3x3 YaspGrid with user-controlled overlap,
> that is periodic in all directions. Then I iterate over the interior partition, and print segment index and ids for all boundaries.
> When I run the program (called periodic_grid_test in my system) with overlap 0, like this:
> 
> ./periodic_grid_test 0 | sort -n
> 
> ... it is easy to see that I get 54 unique indices, [0, ..., 53]. However, with overlap 1, like this:
> 
> ./periodic_grid_test 1 | sort -n
> 
> ... I get only 9 different indices, each repeated 6 times, once for each boundary id.
> The indices are also not consecutive, but numbered 6, 7, 8, 11, 12, 13, 16, 17, 18.
> The same applies with larger overlap (just different actual indices).
> 
> I assumed that these runs would produce identical results, but the do not.
> Have I totally misunderstood the boundary segment indices? Or is there a bug in YaspGrid?
> 
> Any information will be greatly appreciated!
> 
> Atgeirr Flø Rasmussen
> SINTEF ICT
> 
> 
> ----------------- Test program below ---------------------
> 
> #include <dune/grid/yaspgrid.hh>
> #include <cstdlib>
> 
> template <class GridView>
> void investigateBoundary(const GridView& g)
> {
>     const Dune::PartitionIteratorType ptype = Dune::Interior_Partition;
>     typedef typename GridView::template Codim<0>::template Partition<ptype>::Iterator CI;
>     typedef typename GridView::IntersectionIterator FI;
>     for (CI c = g.template begin<0, ptype>(); c != g.template end<0, ptype>(); ++c) {
>         for (FI f = g.ibegin(*c); f != g.iend(*c); ++f) {
>             if (f->boundary()) {
>                 std::cout << f->boundarySegmentIndex() << ' ' << f->boundaryId() << '\n';
>             }
>         }
>     }
> }
> 
> 
> int main(int argc, char** argv)
> {
>     int overlap = (argc > 1 ? std::atoi(argv[1]) : 0);
>     Dune::FieldVector<double, 3> dim(1.0);
>     Dune::FieldVector<int, 3> num(3);
>     Dune::FieldVector<bool, 3> periodic(true);
>     Dune::YaspGrid<3> grid(dim, num, periodic, overlap);
>     investigateBoundary(grid.leafView());
> }
> 
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-- 
Martin Nolte <nolte at mathematik.uni-freiburg.de>

Universität Freiburg                                   phone:
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